The position will be contested during training camp after right tackle Derek Newton was put on the physically unable to perform list last week. Coach Bill O'Brien said Newton would not be returning in 2017.
Giacomini will compete for the right tackle job with veteran Chris Clark, who started in place of Newton and left tackle Duane Brown while each were dealing with injuries last season. While Clark filled in, he did not prove that he can be a starter next season.
Giacomini was drafted by the Green Bay Packers in 2008. He spent his last three seasons playing for the New York Jets before being released in February. Before heading to the Jets, Giacomini played three seasons with the Seattle Seahawks, including the team's 2013 Super Bowl season.